In general, when diffusion is weak a numerical technique must be employed to evaluate \(c\)  when cross-channel gradients in the concentration field are comparable to the cross-channel average.
We call this the “generalised limit”.
In Appendix REF , we identify the regions of parameter space where cross-channel gradients first emerge by perturbing around the cross-channel-averaged concentration, for which \(c_0 = \langle c_0 \rangle (x) + c_0^{\prime }(x,\,y,\,z)\) .
We assume that \(\Vert c_0^{\prime }\Vert \equiv \sqrt{\langle c_0^{\prime 2}\rangle } \ll \langle c_0 \rangle \)  for all \(x\) , seeking to characterise the leading-order effects of shear dispersion in this problem [1]}.
We call this the “weak diffusion limit”.
The validity of this assumption is evaluated a posteriori in Appendix REF .
